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December 2009 A geometric characterization of c-optimal designs for heteroscedastic regression
Holger Dette, Tim Holland-Letz
Ann. Statist. 37(6B): 4088-4103 (December 2009). DOI: 10.1214/09-AOS708


We consider the common nonlinear regression model where the variance, as well as the mean, is a parametric function of the explanatory variables. The c-optimal design problem is investigated in the case when the parameters of both the mean and the variance function are of interest. A geometric characterization of c-optimal designs in this context is presented, which generalizes the classical result of Elfving [Ann. Math. Statist. 23 (1952) 255–262] for c-optimal designs. As in Elfving’s famous characterization, c-optimal designs can be described as representations of boundary points of a convex set. However, in the case where there appear parameters of interest in the variance, the structure of the Elfving set is different. Roughly speaking, the Elfving set corresponding to a heteroscedastic regression model is the convex hull of a set of ellipsoids induced by the underlying model and indexed by the design space. The c-optimal designs are characterized as representations of the points where the line in direction of the vector c intersects the boundary of the new Elfving set. The theory is illustrated in several examples including pharmacokinetic models with random effects.


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Holger Dette. Tim Holland-Letz. "A geometric characterization of c-optimal designs for heteroscedastic regression." Ann. Statist. 37 (6B) 4088 - 4103, December 2009.


Published: December 2009
First available in Project Euclid: 23 October 2009

zbMATH: 1191.62130
MathSciNet: MR2572453
Digital Object Identifier: 10.1214/09-AOS708

Primary: 62K05

Keywords: c-optimal design , Elfving’s theorem , geometric characterization , heteroscedastic regression , locally optimal design , pharmacokinetic models , random effects

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 6B • December 2009
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